Capstone 6940
By Hermela Shimelis
The colon cancer data is a built-in data set in the Survival R package [2]
Data set includes 929 subjects with stage B/C colon cancer who were randomized to three treatment groups then followed for 8-years.
The time to death or progression is given in days. The data set is filtered to evaluate time to death
Objective: Model the relationship between survival time and treatment
| Category | Variables |
|---|---|
| Treatment | Observation (no treatment) |
| Amisole (Lev) | |
| Amisole + 5-FU | |
| Patient Characteristics | Age |
| Sex | |
| Tumor Characteristics | Colon perforation and obstruction |
| Adherence to nearby organs | |
| Tumor differentiation | |
| Local spread | |
| Differentiation of tumor (well, moderate, poor) | |
| More than 4 positive lymph nodes | |
| Other | Time from surgery to registration |
| Observation (%) | Amisole (%) | Amisole + 5-FU (%) | ||
|---|---|---|---|---|
| N=315 | N=310 | N=304 | ||
| Demographics | ||||
| Male | 166 (52.3) | 177 (57.1) | 141 | |
| Median age (years) [IQR] | 60 [53,68] | 61 [53,69] | 61 [52,70] | |
| Cancer characteristics | ||||
| Colon obstruction | 63 (20.0) | 63 (20.3) | 54 (17.8) | |
| Colon perforation | 9 (2.9) | 10 (3.2) | 8 (2.6) | |
| Adherence to nearby organs | 47 (14.9) | 49 (15.8) | 39 (12.8) | |
| Differentiation of tumor | ||||
| Well | 27 (8.6) | 37 (11.9) | 29 (9.5) | |
| Moderate | 236 (74.9) | 229 (73.9) | 221 (72.7) | |
| Poor | 52 (16.5) | 44 (14.2) | 54 (17.8) | |
| Extent of local spread | ||||
| Contiguous | 20 (6.3) | 12 (3.9) | 11 (3.6) | |
| Muscle | 38 (12.1) | 36 (11.6) | 32 (10.5) | |
| Serosa | 249 (79.0) | 259 (83.5) | 251 (82.6) | |
| Submucosa | 8 (2.5) | 3 (1.0) | 10 (3.3) | |
| More than 4 lymph nodes with cancer | Yes | 87 (27.6) | 89 (28.7) | 79 (26.0) |
| Short time from surgery to registration (%) | Yes | 91 (28.9) | 80 (25.8) | 76 (25.0) |
| Characteristic | HR1 | 95% CI1 | p-value |
|---|---|---|---|
| rx | |||
| Obs | — | — | |
| Lev | 0.97 | 0.78, 1.21 | 0.8 |
| Lev+5FU | 0.69 | 0.55, 0.87 | 0.002 |
| Concordance = 0.536 | |||
| 1 HR = Hazard Ratio, CI = Confidence Interval | |||
| Characteristic | HR1 | 95% CI1 | p-value |
|---|---|---|---|
| rx | |||
| Obs | — | — | |
| Lev | 0.98 | 0.79, 1.22 | 0.9 |
| Lev+5FU | 0.69 | 0.54, 0.87 | 0.002 |
| age | 1.01 | 1.00, 1.02 | 0.083 |
| sex | 1.04 | 0.86, 1.26 | 0.7 |
| perfor | 1.00 | 0.59, 1.70 | >0.9 |
| adhere | 1.18 | 0.92, 1.53 | 0.2 |
| surg | 1.27 | 1.03, 1.55 | 0.022 |
| obstruct | 1.33 | 1.06, 1.68 | 0.015 |
| differentiation | |||
| moderate | — | — | |
| poor | 1.43 | 1.13, 1.82 | 0.003 |
| well | 1.08 | 0.78, 1.50 | 0.6 |
| node4 | 2.55 | 2.10, 3.09 | <0.001 |
| local_spread | |||
| contiguous | — | — | |
| muscle | 0.39 | 0.23, 0.64 | <0.001 |
| serosa | 0.64 | 0.43, 0.94 | 0.023 |
| submucosa | 0.29 | 0.10, 0.83 | 0.021 |
| Concordance = 0.674 | |||
| 1 HR = Hazard Ratio, CI = Confidence Interval | |||
| Characteristic | HR1 | 95% CI1 | p-value |
|---|---|---|---|
| rx | |||
| Obs | — | — | |
| Lev | 0.99 | 0.80, 1.23 | >0.9 |
| Lev+5FU | 0.69 | 0.54, 0.87 | 0.002 |
| age | 1.01 | 1.00, 1.02 | 0.069 |
| surg | 1.28 | 1.04, 1.56 | 0.018 |
| obstruct | 1.33 | 1.06, 1.67 | 0.015 |
| differentiation | |||
| moderate | — | — | |
| poor | 1.45 | 1.15, 1.84 | 0.002 |
| well | 1.07 | 0.77, 1.48 | 0.7 |
| node4 | 2.53 | 2.09, 3.07 | <0.001 |
| local_spread | |||
| contiguous | — | — | |
| muscle | 0.37 | 0.23, 0.61 | <0.001 |
| serosa | 0.61 | 0.41, 0.89 | 0.010 |
| submucosa | 0.27 | 0.09, 0.76 | 0.014 |
| Concordance = 0.672 | |||
| 1 HR = Hazard Ratio, CI = Confidence Interval | |||
| chisq | df | p | Variable | |
|---|---|---|---|---|
| rx | 2.335 | 2 | 0.311 | rx |
| age | 0.549 | 1 | 0.459 | age |
| surg | 0.020 | 1 | 0.888 | surg |
| obstruct | 6.148 | 1 | 0.013 | obstruct |
| differentiation | 17.459 | 2 | 0.000 | differentiation |
| node4 | 5.662 | 1 | 0.017 | node4 |
| local_spread | 7.083 | 3 | 0.069 | local_spread |
| GLOBAL | 37.525 | 11 | 0.000 | GLOBAL |
| Characteristic | HR1 | 95% CI1 | p-value |
|---|---|---|---|
| rx | |||
| Obs | — | — | |
| Lev | 0.98 | 0.79, 1.22 | 0.9 |
| Lev+5FU | 0.71 | 0.56, 0.89 | 0.003 |
| age | 1.01 | 1.00, 1.02 | 0.034 |
| surg | 1.30 | 1.06, 1.59 | 0.012 |
| node4 | 2.50 | 2.06, 3.04 | <0.001 |
| local_spread | |||
| contiguous | — | — | |
| muscle | 0.34 | 0.21, 0.56 | <0.001 |
| serosa | 0.58 | 0.39, 0.84 | 0.004 |
| submucosa | 0.24 | 0.08, 0.67 | 0.007 |
| Concordance = 0.674 | |||
| 1 HR = Hazard Ratio, CI = Confidence Interval | |||
| chisq | df | p | Variable | |
|---|---|---|---|---|
| rx | 2.001 | 2 | 0.368 | rx |
| age | 0.670 | 1 | 0.413 | age |
| surg | 0.014 | 1 | 0.905 | surg |
| node4 | 4.288 | 1 | 0.038 | node4 |
| local_spread | 5.298 | 3 | 0.151 | local_spread |
| GLOBAL | 12.411 | 8 | 0.134 | GLOBAL |
| Model | Description | AIC | BIC | C_Index |
|---|---|---|---|---|
| Model 1 | Base model | 5860.383 | 5860.383 | 0.500 |
| Model 2 | Treatment | 5852.236 | 5860.463 | 0.536 |
| Model 3 | Full variables | 5741.401 | 5798.993 | 0.674 |
| Model 4 | Stepwise-selected variables | 5737.261 | 5782.511 | 0.672 |
| Model 5 | Stratified | 4567.829 | 4600.739 | 0.674 |
Original c-index: 0.65
Mean cross-validated c-Index: 0.64
| id: | id |
| study: | 1 for all patients |
| rx: | Treatment - Obs(ervation), Lev(amisole), Lev(amisole)+5-FU |
| sex: | 1=male |
| age: | in years |
| obstruct: | obstruction of colon by tumour |
| perfor: | perforation of colon |
| adhere: | adherence to nearby organs |
| nodes: | number of lymph nodes with detectable cancer |
| time: | days until event or censoring |
| status: | censoring status |
| differ: | differentiation of tumour (1=well, 2=moderate, 3=poor) |
| extent: | Extent of local spread (1=submucosa, 2=muscle, 3=serosa, 4=contiguous structures) |
| surg: | time from surgery to registration (0=short, 1=long) |
| node4: | more than 4 positive lymph nodes |
| etype: | event type: 1=recurrence,2=death |